A rotation-symmetric sample can be divided into asymmetric sections.
An asymmetric section is the maximal volume such that no two points in the volume are related by rotation symmetry.
The rotation symmetry then relates the topological charge in symmetry-related sections.
Because anomalous states always come in pairs (\(Q_\text{tot}=0\) ), asymmetric sections with non-zero topological charge can only exist in systems with even order of rotation symmetry, i.e., \(C_2\) , \(C_4\)  and \(C_6\) .
The anomalous boundary signatures in rotation symmetric topological phases have also been discussed in Refs. [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}.
